One of the major difficulties with mathematical models of staged separation systems is the large dimensionality of the process model. This paper is concerned with simple (reduced-order) steady-state and dynamic models for processes such as distillation, absorption and extraction. The model reduction procedure is based on approximating the composition and flow profiles in the column using polynomials rather than as discrete functions of the stages. The number of equations required to describe the system is thus drastically reduced. The method is developed using a simple absorber system. In the second part of this paper, the application of the method to nonlinear multicomponent separation systems is demonstrated.